In radar systems, where one of the goals is localizing a target, which may be a boat, an aircraft, an automobile, or a subsurface object, a signal (e.g., a propagating electromagnetic or acoustic wave) emanates from the target and arrives at a sensing location. The sensing location may include an array of sensors. Among the goals of the sensing location is often to estimate the relative direction of the target object. For this purpose, the concept of direction of arrival estimation is used to identify the direction of a propagating wave upon its arrival at the sensing location.
Direction of arrival estimation has many practical applications, including finding the direction from which an underwater sound source emanates; localizing objects in the night sky using a radio telescope; in beamforming algorithms in wireless communication systems, including multiple channel access (frequency division multiple access, time division multiple access, code division multiple access); defense applications such as radar and sonar for detecting enemy aircrafts or submarines or other vehicles; locationing in wireless communication networks for detecting user locations in scenarios such as emergency situations; point-to-point microwave for aligning transmit and receive antenna elements to achieve maximum link quality; and in satellite communications for tracking satellite systems.
The Bartlett and Capon algorithms are among methods used in the literature for direction of arrival estimation. The Bartlett algorithm results from a conventional (Fourier or beam-forming) approach to power spectral estimation and the Capon algorithm results from an adaptive approach. Both algorithms make use of an estimated data covariance matrix (EDC), such as the sample covariance matrix (SCM). The Bartlett algorithm relies directly on the EDC, while the Capon approach relies on the inverse of the EDC. When both statistics are made to depend on the same EDC, they are not independent in general.
Other well-known spectral estimation approaches exist, such as the Multiple Signal Classification (MUSIC), Estimation of Signal Parameters via Rotational Invariance Technique (ESPRIT), Maximum-Entropy (ME) [14], etc. A maximum-likelihood (ML) formulation leads to a M-dimensional spectral search algorithm where M is the number of signals present in the data, and therefore can be computationally very expensive. Hence, the focus herein is on approaches, whose search space does not grow with the number of signals present. Among these approaches, the MUSIC algorithm is often regarded as the benchmark performer in direction-of-arrival (DOA) estimation [14]. Indeed, when sources are well-separated, DOA estimates obtained thereby are known to be unbiased and efficient at high signal to noise ratios (SNR). The ability of MUSIC to resolve two closely spaced signals is also known to be slightly better than the Capon-minimum variance distortionless response (MVDR) algorithm [13]. Use of MUSIC, however, requires two important factors, namely perfect knowledge of 1) the total number of signals present, and 2) an eigen-decomposition of the estimated data covariance matrix. The Capon-MVDR algorithm does not require either of these factors, but produces DOA estimates that are consistent (in SNR) and asymptotically efficient (in SNR and sample support only). The Capon-MVDR algorithm requires a matrix inversion of the estimated data covariance, which although computationally expensive, requires fewer computations than a singular value decomposition (SVD) or an Eigen-decomposition. Additionally, the resolution performance of the Capon-MVDR algorithm is only modestly inferior to MUSIC. Hence, the Capon-MVDR algorithm is often attractive in practice.